Traditionally, clipping techniques employ a rectangular window to clip the points, lines and character strings, so that the points, lines and character strings inside the window are shown in the window, and of course, those parts outside the window are not shown. Prior art arrangements are disclosed, for example, in U.S. Pat. No. 4,623,880 and on pages 145 to 153 of "Fundamentals of Interactive Computer Graphics," published by Addison-Wesley Publishing Co. in 1982 and written by Foley & Van Damm.
In the analysis of a point, in the discussion of the above article, a point will be displayed only if it meets the inequalities: EQU Xmin.ltoreq.X.ltoreq.Xmax EQU Ymin.ltoreq.Y.ltoreq.Ymax
where (X,Y) is the coordinate of the point, Xmin and Xmax are the X-coordinate boundaries of the window, and Ymin and Ymax are the Y-coordinate boundaries of the window.
Considering the analysis of lines, in the above article, it is always necessary to perform intersection calculations between lines and every boundary of the clipping window. According to the "Cohen-Sutherland clipping" algorithm, one must divide the surrounded areas of the clipping window into eight sections and then identify those lines that can be trivially accepted or rejected by using region checks. One can easily eliminate the intersection calculations for those lines which satisfy one specific condition, but intersection calculations must still be performed with respect to the other lines. U.S. Pat. No. 4,623,880 discloses a technique to eliminate some intersection calculations for those lines having one endpoint in the window and the other endpoint outside the window. If a line crosses the window and both of its endpoints are outside the window, however, this technique still requires performing the intersection calculations, especially if the graph is very complicated. Such calculations, and the drawing of the lines, is very time consuming. Moreover, the algorithm cannot be used if the clipping window is not rectangular.
With respect to character strings, in accordance with the above article, if the character string is composed of many lines, the character must be treated as if it were a series of lines. If, however, the string is composed of bit-mapped data, a box may be built up to contain each word or the whole string. During clipping, it is only necessary to judge the relationship between the box and the window. If the box is not totally in the clipping window, the complete box (i.e. the word or the character string) will not appear. While the execution speed is increased by this technique, the technique provides incomplete results since some parts of the character string, which are actually within the window, will not be shown.